Single-shot frequency offset measurement with HASTE using the selective parity approach

Measurements of frequency offset are commonly required in MRI. The standard method measures the signal phase as a function of evolution time. Here we use a single shot turbo-spin-echo acquisition method to measure frequency offset at a single evolution time. After excitation the transverse magnetisation evolves during the evolution time, and is then repeatedly refocused. The phase is conjugated between alternate echoes. Using partial parallel acquisition techniques we obtain separate odd- and even- echo images. An iterative procedure ensures self-consistency between them. The difference in phase between the two images yields frequency offset maps. The technique was implemented at 3 Tesla and tested on a healthy human volunteer for a range of evolution times between 6 and 42 ms. A standard method using a similar readout train and multiple evolution times was used as a gold-standard measure. In a statistical comparison with the gold standard no evidence for bias or offset was found. There was no systematic variation in precision or accuracy as a function of evolution time. We conclude that the presented approach represents a viable method for the rapid generation of frequency offset maps with a high image quality and minimal distortion.


Materials and methods
The original Siemens diffusion-weighted HASTE pulse sequence as a variant of the HASTE method was modified through implementing a variable evolution time between the 90° excitation and the first 180° refocusing RF pulses, and removing the diffusion encoding preparation module.Although this sequence is termed 'HASTE' it uses centre-out phase-encoding, and the readout is as described in Norris et al 4 .To avoid artefacts arising from the non-CPMG condition due to the evolution of spins during the evolution time, a displacing gradient was used prior to each read-out gradient to remove the odd parity echo out of the acquisition window, and only the even parity echo was acquired at each echo time (Fig. 2A).For stabilisation of the early echo amplitudes, the use of a minimum of four dummy cycles was necessary before the readout train (not shown in Fig. 2A).This sequence was used to obtain a gold standard measurement using the classical approach of incrementing the evolution time between the excitation pulse and the readout, and calculating the frequency offset as the slope of the phase as a function of τ.These data could then be compared to those obtained by the selective parity (SP) method.
The main experiment was implemented using the SP-HASTE method 12 .The pulse sequence was slightly modified compared to HASTE by applying displacement gradients either before or after the read-out gradient to acquire the echo parities in an alternating fashion (Fig. 2B), and by no longer applying dummy cycles.A phase graph showing how different coherence pathways combine to form the odd and even parity echoes is shown in Fig. 2 of Norris 12 .
In the SP-HASTE method, Shinnar le Roux refocusing RF pulses 14 replaced the original truncated sinc refocusing RF pulses.Their superior slice profiles result in a smooth signal intensity decay over early echoes.This makes the use of dummy cycles for the echo amplitude stabilisation unnecessary leading to a shorter echo time and higher signal intensity.Better slice profiles of the SLR RF pulses come at the cost of a higher specific absorption rate (SAR) contribution, which was compensated by using a smooth transition between pseudo steady states (TRAPS 15,16 , Fig. 3A) for the later echoes.A centre-out phase encoding scheme was also employed to sample the k-space with evenly distributed odd and even echo parities (Fig. 3B).
MRI scans were performed on a whole body 3T Siemens Prisma/PrismaFit scanner (80 mT/m strength and 200 mT/m/ms slew rate) with a 32-channel receive-only head coil in one healthy female volunteer.Ethical approval was provided by the local ethics committee METC Oost-Nederland, which is an accredited Dutch ethical reviewing board.The approval is registered under CMO2014/288 entitled 'Imaging Human Cognition' .Informed written consent was obtained.All experiments were performed in accordance with the relevant guidelines and regulations.Common acquisition parameters were as follows: TR = 2000 ms , FOV = 200 × 200 mm, matrix size of 64 × 64, 3.1 mm isotropic in-plane resolution, three axially oriented 3 mm slices, and 20 repetitions for the SP-HASTE method.No accelerated imaging was used for the data collection.Data were collected with evolution times ranging from 0 to 42 ms with increments of 6 ms.TE was 34.65 ms and 6.93 ms for the HASTE and SP-HASTE, respectively.The echo spacing was 6.93 ms for both sequences.The longer TE was necessitated by the presence of the four dummy cycles.

Reconstruction
The HASTE data were reconstructed using the standard reconstruction algorithm delivered by the manufacturer.A novel reconstruction approach was used for the SP-HASTE data to allow separate reconstruction of odd and even parity images using in-house code written in matlab (MATLAB and Statistics Toolbox Release 2012b, The MathWorks, Inc., Natick, Massachusetts, United States).The acquired echo parities were used to create two separate k-spaces (Fig. 4), one for each parity.The odd and even k-space missing lines were then estimated through SPIRiT (GRAPPA) algorithm 17 .RF single loop receiver coils have an inhomogeneous reception field and a spatially varying receiver field with an arbitrary phase relationship to the orientation of the transmit field.By reference to Fig. 1, the odd and even parity images are complex conjugates of each other in the image domain considering the CPMG angle as the frame of reference.An iterative process was then used to ensure that the final images satisfied this condition.This iterative approach converges to a consistent representation of the non-acquired data lines as is depicted in Fig. 5.The critical step is the estimation of the CPMG phase map (step 3), which is subsequently used to convert odd parity to even parity data and vice versa (step 4).The information from both echo parities is then combined in step 5.After ~ 30 iterations (relative error below 1%), odd parity and even parity images eventually converge to the same solution, providing identical magnitude images.The final magnitude images were generated using the sum of squares of the coil images.For frequency offset (FO) mapping, SEPIA, a Quantitative Susceptibility Map (QSM) software 18 was used to unwrap the phase data using the SEGUE method 19 , and generate the phase images for both the Siemens and the selective parity data.

Results
For the modified SP-HASTE sequence, the 0 ms delay time was disregarded since no phase shift is generated between the odd and even parity echoes.The FO maps were generated using Eq.(1): where ɸ e and ɸ o are the even and odd parity phase images, respectively, and τ is the evolution time.The FO maps created with HASTE and from single shot SP-HASTE acquisitions at different evolution times are presented in Fig. 6.
By collecting multiple repetitions of the SP-HASTE we can explore whether there is a systematic difference in the FO values recorded when taking HASTE as a gold-standard measure, as averaging over the repetitions should ensure sufficient SNR that systematic errors become visible.To this end a linear regression was performed for the FO mean values obtained with the SP-HASTE for all evolution times versus the FO mean value from the HASTE method.For the SP-HASTE method, FO values were averaged over 20 repetitions.Table 1 shows that differences in the slope between the two techniques were less than 6% for all evolution times (0.94 < slope < 1.06) and that the offset was in all cases less than 3 Hz.The corresponding data are shown in Fig. 7.
For the HASTE measurements the standard deviation could be calculated from the measured slope and for the SP-HASTE it could be obtained from the variance over the repetitions.Calculated Std maps are presented in Fig. 8 for the FO maps obtained with the HASTE and SP-HASTE.Overall, similar standard deviation values are observed.Slightly higher Std values are observable for the SP-HASTE FO maps obtained from 6 to 24 ms evolution times which reflect more fluctuation between the measurements for these evolution times.
Figure 9 illustrates the difference between the FO values estimated with the two methods for all the evolution times for slice 1.The smallest median difference was found for 6 ms and 18 ms evolution times, with the FO difference close to 0 Hz.The largest median difference was for 36 ms delay time with a median difference of 2.62 Hz.The evolution times which showed the narrowest whiskers were 18 ms and 42 ms.

Discussion
In this paper we have demonstrated that a single shot non-CPMG HASTE sequence that acquires both odd and even parities of echoes is capable of generating field maps with the same precision and accuracy as the slower standard method.This capability could have application in generating undistorted FO maps for EPI distortion correction, and for monitoring temperature changes, for example in hyperthermia.This approach relies on obtaining separate images corresponding to the two parities of echo, and relies on the complex conjugate relationship between the echo parities at the voxel level.CP sequences that acquire the two parities in an alternating fashion are an obvious choice for such an experiment as demonstrated herein, but a two echo asymmetrical spin-echo EPI experiment could also be used to generate similar maps.If it is not possible or desirable to use parallel imaging techniques to generate separate OP and EP images then they could be obtained in two separate acquisitions.The resultant FO map would be generated under the assumption that the phase was stable between the two scans.It would also be necessary to insert dummy scans as in the standard method to avoid fluctuations in the echo intensity 4 .An alternative two-shot approach that would be less sensitive to motion-induced phase variation would be to collect a reference phase map using a CPMG sequence (evolution time of zero) and compare this with the phase of an OP/EP acquisition.One slight surprise in the results obtained was the relative insensitivity of the FO maps to the additional delay.Increasing the delay time will increase the phase evolution which will be a linear effect, while reducing the SNR, which will decay with T 2 * .We chose the range of evolution times to have a good coverage up to and beyond the anticipated T 2 * , but it would seem that at 3 T a delay of 6 ms is already sufficient to generate high quality FO maps.The rapid advance of denoising techniques 20 that reduce the thermal noise contribution can potentially reduce the minimum usable delay still further.
In this work we examined the phase evolution under the influence of static magnetic field inhomogeneities in the brain at 3 T. Different organs, higher static magnetic field strengths, or the presence of metallic implants would all present a greater challenge.If the frequency offset would be caused by chemical shift then the frequency could change abruptly with spatial position, and the maximum phase difference that could be allowed to evolve should not exceed π.If the frequency offsets are caused by susceptibility differences then there will be a continuous gradient in the frequency offset, and within the constraints of phase-unwrapping algorithms, this can be unwrapped and phase evolutions > π within a voxel corrected.
In comparison with the commonly used multi-echo gradient-echo approach the current method has the advantage that it does not conflate the imaging parameters with the evolution of the magnetisation.In the multiecho approach a large frequency offset could require a short inter-echo spacing and conversely measurement of small frequency offsets can prolong the echo train and increase the acquisition time.One further advantage of the current method is that there is no minimum TE, so in the presence of strong inhomogeneities there is no minimum evolution time: if signal can be excited then its frequency offset can be measured.The present approach will work less well for tissue with short T2 and will also have higher RF power deposition.It could prove particularly attractive for applications at low static magnetic field where field homogeneity is poor.
In conclusion, we have demonstrated a novel approach for mapping frequency offset that removes the requirement to measure at multiple evolution times, and offers the prospect of accurate single shot measurement with high image quality and negligible distortion.

Figure 1 .
Figure 1.Schematic showing how the odd-and even-parity echoes are bisected by the reference phase in a CP sequence for any arbitrary voxel.The assignment of OP/EP is arbitrary.The orientation of R is determined by the sensitivity profile of the receiver coil relative to the transmit field and will vary for any given voxel and receiver coil.

Figure 2 .
Figure 2. The timing diagram of (A) HASTE, (B) SP-HASTE methods: a variable evolution time was implemented between the excitation and the first refocusing RF pulses.Displacing gradients, as depicted by asterisks, were used to acquire the parity of interest and avoid destructive interference between parities.Only the RF pulse train and frequency encoding direction for the first 2 echoes are shown.Dummy echoes are not shown for HASTE timing diagram in (A).

Figure 3 .
Figure 3. SP-HASTE: (A) TRAPS to reduce the SAR contribution from SLR refocusing pulses.The k-space centre is sampled using nominally 180° pulses, and then, the nutation angle is reduced to a fixed low flip angle of 140°.(B) The centre-out phase encoding scheme to sample the k-space while alternating echo parities, starting with the odd echo parity for the k-space central line (white indicates acquired data).

Figure 4 .
Figure 4.Even and odd echo parity k-spaces created in the reconstruction: undersampled lines can be seen in the original k-spaces (top row).The bottom row shows the odd and even parity k-spaces with the missing lines estimated through the SPIRiT algorithm.

Figure 5 .
Figure 5. Schematic of the SP-HASTE reconstruction performed for each receiver element.The OP and EP data are separated and missing k-space lines are filled using SPIRiT (step 1).Transformation into the image domain (step 2) results in two images that should have a complex conjugate relationship defined relative to the CPMG angle.An estimate of the CPMG angle is obtained as the angle bisecting the OP and EP phases in each voxel (step 3).Using this estimate of the CPMG phase angle it is then possible to transform OP data to EP data and vice versa generating pseudo OP and EP data (step 4).The original and pseudo data are then averaged (step 5) and transformed back into k-space (step 6).Data consistency is enforced by restoring the originally acquired data for each parity (step 7).If the resulting magnitude images are identical to within 1% tolerance the procedure is terminated (step 8) or a new iteration is performed.

Figure 6 .
Figure 6.Left, frequency offset maps created with the HASTE (top) and single shot SP-HASTE (2nd row down) methods: FO maps from the SP-HASTE methods were calculated for different evolution times from one repetition.Grey scale units are expressed in Hz.In the right column the difference between the two is shown (HASTE-SP-HASTE).

Figure 7 .Figure 8 .
Figure 7. Linear regression of the FO values obtained with the SP-HASTE (vertical axes) versus those obtained with HASTE (horizontal axes) for the same sample axial slices as in Fig. 6 (top to bottom) for different evolution times (left to right).The red solid line on each panel represents the calculated slope.The blue dots are the individual data points (voxels within slice).Each data point for SP-HASTE represents the mean over 20 repetitions.Units are expressed in Hz.

Figure 9 .
Figure 9. Box plot of the difference between the FO values estimated using the SP-HASTE and HASTE for slice 1 as shown in Fig. 6 for all the evolution times, calculated on a pixel by pixel basis.

Table 1 .
Slope and intercept values as a function of evolution time.The predicted linear regression slope and intercept for slice 1: linear regression was performed for the FO mean values obtained with SP-HASTE for evolution times ranging from 6 to 42 ms vs. the FO mean value from the HASTE.